Mike's Water Container

I approach this problem in a more intuitive manner. Since we know that the end result is 34 pints, just work BACKWARDS. Day 4 - They consumed 60%. and left 34 pints. Therefore, x-0.6x=34 and x= 85 pints at the start of Day 4. Day 3- They consumed 3/8th. Therefore, x-3/8x=85 pints. x= 136 pints , the amount they started with on Day 3. Day 2- They consumed 15%. Therefore, x-0.15x=136 pints. x= 160 pints, the amount they started with on Day 2. Day 1- The family drank 1/5th. Therefore, x- x/5 = 160 pints. x= 200 pints, the amount to begin with on Day 1. Convert 200 pints to gallon which gives you 25.

Consider the water container as a whole, which is 100%, which equals 1.

Then on the first day, used 1/5, which is 20%, you subtract it from 1, and you get 0.8 or 80%.

On the second day, used 15% of the previous day's remaining 80%, you can do it by 80%*(1-15%)=0.68 or 68%.

On the third day, used 3/8 of the previous day's remaining, apply similar math: 68%*(1-3/8)=0.425 or 42.5%.

On the fourth day, used 60% of the previous day's remaining, calculate 42.5%*(1-60%)=0.17 or 17%.

And that 17% is what you get left in the water container at the end of fourth day, and since the question tells you that before anyone drinks on the the fifth day, there are 34 pints of water left which is corresponding to the 17% of the original.

You can set up a ratio equation to solve it (17% versus 100% equals 34 pints versus ? pints) or just do division 34/0.17=200 pints.

However the question asks for how many gallons, so at last you convert pints into gallons, which the conversion between them is 8 pints=1 gallon, so you do division again: 200/8= 25 gallons.